Question: Solve for $x$ and $y$ using elimination. ${3x+2y = 26}$ ${2x-2y = 14}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $5x = 40$ $\dfrac{5x}{{5}} = \dfrac{40}{{5}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {3x+2y = 26}\thinspace$ to find $y$ ${3}{(8)}{ + 2y = 26}$ $24+2y = 26$ $24{-24} + 2y = 26{-24}$ $2y = 2$ $\dfrac{2y}{{2}} = \dfrac{2}{{2}}$ ${y = 1}$ You can also plug ${x = 8}$ into $\thinspace {2x-2y = 14}\thinspace$ and get the same answer for $y$ : ${2}{(8)}{ - 2y = 14}$ ${y = 1}$